A consistent $\mathcal{O}(v^2)$ NRQCD description of decays and high-$P_T$ prompt production of charmonia

Abstract

We present a global determination of the six long-distance matrix elements (LDMEs) within non-relativistic QCD (NRQCD) appearing in the production of prompt $J/\psi$ up to $\mathcal{O}(v^2)$ using high-$P_T$ LHC data for direct and feed-down contributions from $\chi_c$ and $\psi(2S)$. Using a leading-power fragmentation framework at NLO+NLL, we fit $\psi(2S)/J/\psi$ yield ratios from ATLAS and CMS and $\psi(2S)$ CMS polarization data at $\sqrt{s} = 13$ TeV, injecting one decay width per charmonium. The fit LDMEs provide excellent predictions of the CMS and ATLAS cross-section data up to $P_T=360$ GeV for the $J/\psi$, as well as the $J/\psi$ polarization data from CMS. The obtained excellent agreement with production and decay data demonstrates that $\mathcal{O}(v^2)$ NRQCD is sufficient to describe $J/\psi$, $\psi(2S)$, and $\chi_c$ hadroproduction at large $P_T$.